Question:
How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?
Correct Answer
$5650
Solution And Explanation
Solution
Given,
Amount (A) = $7062.5
Rate of Simple Interest (R) = 5%
Time (T) = 5 years
Thus, Principal (P) = ?
Method (1) Using Formula
Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given
Formula to find the Principal (P)
Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)
⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]
⇒ A = P (1 + RT)
Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given
In the given question, we need to find the Principal (P)
Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get
$7062.5 = P (1 + 5% × 5)
⇒ $7062.5 = P (1 + 5/100 × 5)
⇒ $7062.5 = P (1 + 5 × 5/100)
⇒ $7062.5 = P (1 + 25/100)
⇒ $7062.5 = P (100 + 25/100)
⇒ $7062.5 = P × 125/100
⇒ P × 125/100 = $7062.5
⇒ P = 7062.5/125/100
⇒ P = 7062.5 × 100/125
⇒ P = 7062.5 × 100/125
⇒ P = 706250/125
⇒ P = $5650
Thus, the sum borrowed (P) = $5650 Answer
Method (1) Using Unitary Method
Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given
Calculation of the Simple Interest
Let, the principal = 100
Here, since rate of simple interest = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
Calculation of the Amount
Since, in the question, time = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 7062.5, then the Principal = 100/125 × 7062.5
= 100 × 7062.5/125
= 706250/125
= 5650
Thus, Principal = $5650
Thus, the sum borrowed = $5650 Answer
Similar Questions
(1) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8970 to clear it?
(2) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?
(3) If Lisa paid $4374 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?
(5) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?
(7) How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?
(8) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 4 years.
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 3 years.